In Assassin's Creed: Odyssey Fate of Atlantis you'll encounter a few opportunities to romance. Your decision to romance or not does not influence your relations with the given hero. Romance is only a short scene that does not influence the gameplay.
During the third mission (A Lover and A Fighter) in Assassin's Creed: Odyssey Fate of Atlantis you'll encounter Adonis. They will give you a mission to cripple Persephone's control over the area.
To do that, travel to the Fortress of the Three Sisters. When you clear the area, you'll receive the location of Aegea the Amazonian Queen.
Kill the commander and return to Adonis to finish the mission.
During the next conversation, you'll receive the option to romance. It is marked with a heart icon. If you choose the option, you'll begin a romance with Adonis.